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0,70000

0,80000

0,57143

As an application, the values of (3 and of (4 were calculated in analogy to that was developed for case bi). The resulting values are given in Table 6.5.

Table 6.5. ß3 and ß4 values for rectangular diagram

Rectangular costitutive law

Table 6.5. ß3 and ß4 values for rectangular diagram

Rectangular costitutive law

x/

fck - 50 N/mm2

fck - 55 N/mm2

fck - 60 N/mm2

fck - 70 N/mm2

fck - 80 N/mm2

fck - 90 N/mm2

/h

ß3

ß4

ß3

ß4

ß3

ß4

ß3

ß4

ß3

ß4

ß3

ß4

1,00

0,80000

0,40000

0,76781

0,39375

0,73625

0,38750

0,67500

0,37500

0,61625

0,36250

0,56000

0,35000

1,20

0,88889

0,44444

0,85601

0,43898

0,82344

0,43339

0,75938

0,42188

0,69695

0,40997

0,63636

0,39773

1,40

0,92308

0,46154

0,89154

0,45720

0,86011

0,45269

0,79773

0,44318

0,73623

0,43308

0,67586

0,42241

1,60

0,94118

0,47059

0,91073

0,46704

0,88030

0,46332

0,81964

0,45536

0,75946

0,44674

0,70000

0,43750

1,80

0,95238

0,47619

0,92274

0,47320

0,89308

0,47004

0,83382

0,46324

0,77482

0,45577

0,71628

0,44767

2,00

0,96000

0,48000

0,93097

0,47742

0,90191

0,47469

0,84375

0,46875

0,78572

0,46219

0,72800

0,45500

2,50

0,97143

0,48571

0,94341

0,48380

0,91534

0,48176

0,85909

0,47727

0,80282

0,47225

0,74667

0,46667

5,00

0,98824

0,49412

0,96191

0,49329

0,93554

0,49239

0,88269

0,49038

0,82975

0,48809

0,77677

0,48548

6.1.2 Calculation of strength of rectangular section 6.1.2.1 Determination of NRd and MRd

Given a transverse rectangular section with symmetrical geometry and reinfocement, the reinforcing bars, the materials and the line that defines the deformed configuration at ultimate limit states, the design normal force and the design bending moment are determined about the centroidal axis.

V Nc

V Nc

Figure 6.2. Rectangular section at ultimate limit state

Figure 6.2. Rectangular section at ultimate limit state

On the hypothesis that straight sections remain straight, deformation are as in fig. 6.2. On the basis of their level from the stress-strain diagrams of concrete and steel, the corresponding stresses are calculated.

In order to determine NRd and MRd two equations of equilibrium (horizontal shift and rotation) are written.

Equilibrium to shift: if Nc is the resultant of compressive stresses applied to concrete, N's the resultant of stresses applied to the compressed reinforcing bars A's and Ns the resultant of traction in the reinforcing bars As , NRd = Nc + N's - Ns

The single terms can be developed as: Nc =-b-ßi-x-fcd N's = -a's'A's Ns = Gs'As

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